Universal Planckian dissipation in the strange metal state of the cuprates

Arkady Shekhter, B. J. Ramshaw, M. K. Chan, N. Harrison

A major puzzle in high-Tc superconductivity is the origin of the “Planckian” relaxation rate 1/τ underlying the linear-in-temperature resistivity in the strange-metal state, which persists up to very high temperatures. Implicit in theoretical discussions is the assumption that 1/τ must be universal. Experimentally, it is unclear, however, how such universality can be reconciled with the observed strong doping dependence of the resistivity over a wide doping range. We show, through an analysis of a large body of optical conductivity and electrical resistivity data, that a universal 1/τ requires only that the square optical plasma frequency $${\omega }_{{{\rm{opt}}}}^{2}(p)$$ scales linearly with hole doping p across the entire doping range, as is observed experimentally. We further argue that this can be understood via a Gutzwiller factor in doped Mott insulators of the form proposed by Anderson. Through an analysis of existing data, the authors show that the “Planckian” relaxation rate in cuprate superconductors is doping independent. This follows from the finding that the square optical plasma frequency scales linearly with doping, which they further argue is a natural consequence of Mott physics.